Question

Determine the null and alternative hypotheses. Choose the correct answer below. A. H0​: The distribution of colors is not the same as stated by the manufacturer. H1​: The distribution of colors is the same as stated by the manufacturer. B. H0​: The distribution of colors is the same as stated by the manufacturer. H1​: The distribution of colors is not the same as stated by the manufacturer. C. None of these. Compute the expected counts for each color. Color Frequency Expected Count Brown 62 nothing Yellow 64 nothing Red 53 nothing Blue 59 nothing Orange 83 nothing Green 63 nothing ​(Round to two decimal places as​ needed.) What is the test​ statistic? chi Subscript 0 Superscript 2 equals nothing ​(Round to three decimal places as​ needed.) What is the​ P-value of the​ test? ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Based on the​ results, do the colors follow the same distribution as stated in the​ problem? A. Reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. B. Do not reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. C. Reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. D. Do not reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

Colored Candies in a bag

Color	Brown	Yellow	Red	Blue	Orange	Green
Frequency	6262	6464	5353	5959	8383	6363
Claimed Proportion	0.130.13	0.140.14	0.130.13	0.240.24	0.200.20	0.16

Answer 1

(first part) Determine the null and alternative hypotheses. Choose the correct answer below.

right choice is B.

H0​: The distribution of colors is the same as stated by the manufacturer.

H1​: The distribution of colors is not the same as stated by the manufacturer.

(second part) Compute the expected counts for each color.

Color	Brown	Yellow	Red	Blue	Orange	Green	Total
Expected frequency(E)=n*p	49.92	53.76	49.92	92.16	76.8	61.44	384

(third part) What is the test​ statistic? chi Subscript 0 Superscript 2 equals nothing ​(Round to three decimal places as​ needed.)

here we use chi-square test and statistic sum(O-E)2/E=17.535 with k-1=6-1=5 df

Color	Brown	Yellow	Red	Blue	Orange	Green	Total
Observed Frequency (O)	62	64	53	59	83	63	n=384
Claimed Proportion (p)	0.13	0.14	0.13	0.24	0.2	0.16	1
Expected frequency(E)=n*p	49.92	53.76	49.92	92.16	76.8	61.44	384
(O-E)	12.08	10.24	3.08	-33.16	6.2	1.56	0
(O-E)2/E	2.923	1.950	0.190	11.931	0.501	0.040	17.535

(fourth part) What is the​ P-value of the​ test? ​P-valueequals nothing ​(Round to three decimal places as​ needed.)

p-value= 0.004 ( using ms-excel =chidist(17.535,5)

(fifth part) Based on the​ results, do the colors follow the same distribution as stated in the​ problem?

right choice is A. Reject H0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

since the p-value=0.004 is less than typical level of significance alpha=0.05 ( generally alpha=0.05 is taken if it is not mentioned) so we Reject H0 in favor of alternate hypothesis H1.